Thank you all for your responses. I guess I should have clarified my initial thoughts in my posting although I appreciate the insight/advice from all.
My initial reaction was to end the lease at the date they had requested which would give them approximately one month to clear things out at while making repairs that may be necessary and/or marketing the apartment. My only request was the covering of the brokers fee which is equal to one months rent unless they were able to find me a qualified tenant in which case no fee would need to be paid and if no repairs needed to be done then they obviously would get the security deposit back as well. If they were able to get moved out earlier than they expected, I would also refund them the additional days of rent that was already paid.
I wasn't thinking of asking them to cover loss income until someone that I spoke to mentioned it to me. After speaking to a few landlords, attorneys and friend's that I know in which some had similar thoughts to those above but more than one mentioned the loss of income. While the rational was to take the emotions out of the equation and I can respect that, my gut was telling me exactly what everyone above basically posted.
I lost a very good client of mine the same day that I lost my tenant and while landlording is a business its not my livelihood. A few extra dollars isn't going to change anything on my end. I just wanted to see what the opinions/experience was of fellow BPer's were since I previously heard two different sides of the spectrum. I am fairly new to this industry and have never had an experience like this in the past nor has anyone that I have known.
@Deanna McCormick - How does one deal with the refund of the security deposit if the tenant is deceased and the daughter who co-signed is not on the lease? One daughter had asked me to give it back to the co-signer (different daughter). Is this what is typically done?
Thank you again everyone for the advice.